TSTP Solution File: REL035-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL035-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:44:21 EDT 2023
% Result : Unsatisfiable 16.76s 2.52s
% Output : Proof 17.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL035-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 21:48:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 16.76/2.52 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 16.76/2.52
% 16.76/2.52 % SZS status Unsatisfiable
% 16.76/2.52
% 17.09/2.61 % SZS output start Proof
% 17.09/2.61 Axiom 1 (composition_identity_6): composition(X, one) = X.
% 17.09/2.61 Axiom 2 (goals_14): composition(sk1, top) = sk1.
% 17.09/2.61 Axiom 3 (maddux1_join_commutativity_1): join(X, Y) = join(Y, X).
% 17.09/2.61 Axiom 4 (converse_idempotence_8): converse(converse(X)) = X.
% 17.09/2.61 Axiom 5 (def_top_12): top = join(X, complement(X)).
% 17.09/2.61 Axiom 6 (def_zero_13): zero = meet(X, complement(X)).
% 17.09/2.61 Axiom 7 (converse_multiplicativity_10): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 17.09/2.61 Axiom 8 (composition_associativity_5): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 17.09/2.61 Axiom 9 (converse_additivity_9): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 17.09/2.61 Axiom 10 (maddux2_join_associativity_2): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 17.09/2.61 Axiom 11 (maddux4_definiton_of_meet_4): meet(X, Y) = complement(join(complement(X), complement(Y))).
% 17.09/2.61 Axiom 12 (composition_distributivity_7): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 17.09/2.61 Axiom 13 (converse_cancellativity_11): join(composition(converse(X), complement(composition(X, Y))), complement(Y)) = complement(Y).
% 17.09/2.61 Axiom 14 (maddux3_a_kind_of_de_Morgan_3): X = join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y))).
% 17.09/2.61
% 17.09/2.61 Lemma 15: complement(top) = zero.
% 17.09/2.61 Proof:
% 17.09/2.61 complement(top)
% 17.09/2.61 = { by axiom 5 (def_top_12) }
% 17.09/2.61 complement(join(complement(X), complement(complement(X))))
% 17.09/2.61 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.09/2.61 meet(X, complement(X))
% 17.09/2.61 = { by axiom 6 (def_zero_13) R->L }
% 17.09/2.61 zero
% 17.09/2.61
% 17.09/2.61 Lemma 16: join(X, join(Y, complement(X))) = join(Y, top).
% 17.09/2.61 Proof:
% 17.09/2.61 join(X, join(Y, complement(X)))
% 17.09/2.61 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.61 join(X, join(complement(X), Y))
% 17.09/2.61 = { by axiom 10 (maddux2_join_associativity_2) }
% 17.09/2.61 join(join(X, complement(X)), Y)
% 17.09/2.61 = { by axiom 5 (def_top_12) R->L }
% 17.09/2.61 join(top, Y)
% 17.09/2.61 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.61 join(Y, top)
% 17.09/2.61
% 17.09/2.61 Lemma 17: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 17.09/2.61 Proof:
% 17.09/2.61 converse(composition(converse(X), Y))
% 17.09/2.61 = { by axiom 7 (converse_multiplicativity_10) }
% 17.09/2.61 composition(converse(Y), converse(converse(X)))
% 17.09/2.61 = { by axiom 4 (converse_idempotence_8) }
% 17.09/2.61 composition(converse(Y), X)
% 17.09/2.61
% 17.09/2.61 Lemma 18: composition(converse(one), X) = X.
% 17.09/2.61 Proof:
% 17.09/2.61 composition(converse(one), X)
% 17.09/2.61 = { by lemma 17 R->L }
% 17.09/2.61 converse(composition(converse(X), one))
% 17.09/2.61 = { by axiom 1 (composition_identity_6) }
% 17.09/2.61 converse(converse(X))
% 17.09/2.61 = { by axiom 4 (converse_idempotence_8) }
% 17.09/2.61 X
% 17.09/2.61
% 17.09/2.61 Lemma 19: join(complement(X), composition(converse(Y), complement(composition(Y, X)))) = complement(X).
% 17.09/2.61 Proof:
% 17.09/2.61 join(complement(X), composition(converse(Y), complement(composition(Y, X))))
% 17.09/2.61 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.61 join(composition(converse(Y), complement(composition(Y, X))), complement(X))
% 17.09/2.61 = { by axiom 13 (converse_cancellativity_11) }
% 17.09/2.61 complement(X)
% 17.09/2.61
% 17.09/2.61 Lemma 20: join(complement(X), complement(X)) = complement(X).
% 17.09/2.62 Proof:
% 17.09/2.62 join(complement(X), complement(X))
% 17.09/2.62 = { by lemma 18 R->L }
% 17.09/2.62 join(complement(X), composition(converse(one), complement(X)))
% 17.09/2.62 = { by lemma 18 R->L }
% 17.09/2.62 join(complement(X), composition(converse(one), complement(composition(converse(one), X))))
% 17.09/2.62 = { by axiom 1 (composition_identity_6) R->L }
% 17.09/2.62 join(complement(X), composition(converse(one), complement(composition(composition(converse(one), one), X))))
% 17.09/2.62 = { by axiom 8 (composition_associativity_5) R->L }
% 17.09/2.62 join(complement(X), composition(converse(one), complement(composition(converse(one), composition(one, X)))))
% 17.09/2.62 = { by lemma 18 }
% 17.09/2.62 join(complement(X), composition(converse(one), complement(composition(one, X))))
% 17.09/2.62 = { by lemma 19 }
% 17.09/2.62 complement(X)
% 17.09/2.62
% 17.09/2.62 Lemma 21: join(top, complement(X)) = top.
% 17.09/2.62 Proof:
% 17.09/2.62 join(top, complement(X))
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 join(complement(X), top)
% 17.09/2.62 = { by lemma 16 R->L }
% 17.09/2.62 join(X, join(complement(X), complement(X)))
% 17.09/2.62 = { by lemma 20 }
% 17.09/2.62 join(X, complement(X))
% 17.09/2.62 = { by axiom 5 (def_top_12) R->L }
% 17.09/2.62 top
% 17.09/2.62
% 17.09/2.62 Lemma 22: join(top, X) = join(Y, top).
% 17.09/2.62 Proof:
% 17.09/2.62 join(top, X)
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 join(X, top)
% 17.09/2.62 = { by lemma 21 R->L }
% 17.09/2.62 join(X, join(top, complement(X)))
% 17.09/2.62 = { by lemma 16 }
% 17.09/2.62 join(top, top)
% 17.09/2.62 = { by lemma 16 R->L }
% 17.09/2.62 join(Y, join(top, complement(Y)))
% 17.09/2.62 = { by lemma 21 }
% 17.09/2.62 join(Y, top)
% 17.09/2.62
% 17.09/2.62 Lemma 23: join(X, top) = top.
% 17.09/2.62 Proof:
% 17.09/2.62 join(X, top)
% 17.09/2.62 = { by lemma 22 R->L }
% 17.09/2.62 join(top, complement(top))
% 17.09/2.62 = { by axiom 5 (def_top_12) R->L }
% 17.09/2.62 top
% 17.09/2.62
% 17.09/2.62 Lemma 24: converse(join(converse(X), Y)) = join(X, converse(Y)).
% 17.09/2.62 Proof:
% 17.09/2.62 converse(join(converse(X), Y))
% 17.09/2.62 = { by axiom 9 (converse_additivity_9) }
% 17.09/2.62 join(converse(converse(X)), converse(Y))
% 17.09/2.62 = { by axiom 4 (converse_idempotence_8) }
% 17.09/2.62 join(X, converse(Y))
% 17.09/2.62
% 17.09/2.62 Lemma 25: converse(top) = top.
% 17.09/2.62 Proof:
% 17.09/2.62 converse(top)
% 17.09/2.62 = { by lemma 23 R->L }
% 17.09/2.62 converse(join(converse(top), top))
% 17.09/2.62 = { by lemma 24 }
% 17.09/2.62 join(top, converse(top))
% 17.09/2.62 = { by lemma 22 }
% 17.09/2.62 join(X, top)
% 17.09/2.62 = { by lemma 23 }
% 17.09/2.62 top
% 17.09/2.62
% 17.09/2.62 Lemma 26: join(meet(X, Y), complement(join(complement(X), Y))) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 join(meet(X, Y), complement(join(complement(X), Y)))
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.62 join(complement(join(complement(X), complement(Y))), complement(join(complement(X), Y)))
% 17.09/2.62 = { by axiom 14 (maddux3_a_kind_of_de_Morgan_3) R->L }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 27: join(zero, meet(X, X)) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 join(zero, meet(X, X))
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.62 join(zero, complement(join(complement(X), complement(X))))
% 17.09/2.62 = { by axiom 6 (def_zero_13) }
% 17.09/2.62 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 17.09/2.62 = { by lemma 26 }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 28: join(zero, zero) = zero.
% 17.09/2.62 Proof:
% 17.09/2.62 join(zero, zero)
% 17.09/2.62 = { by lemma 15 R->L }
% 17.09/2.62 join(zero, complement(top))
% 17.09/2.62 = { by lemma 15 R->L }
% 17.09/2.62 join(complement(top), complement(top))
% 17.09/2.62 = { by lemma 20 }
% 17.09/2.62 complement(top)
% 17.09/2.62 = { by lemma 15 }
% 17.09/2.62 zero
% 17.09/2.62
% 17.09/2.62 Lemma 29: join(zero, join(zero, X)) = join(X, zero).
% 17.09/2.62 Proof:
% 17.09/2.62 join(zero, join(zero, X))
% 17.09/2.62 = { by axiom 10 (maddux2_join_associativity_2) }
% 17.09/2.62 join(join(zero, zero), X)
% 17.09/2.62 = { by lemma 28 }
% 17.09/2.62 join(zero, X)
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.62 join(X, zero)
% 17.09/2.62
% 17.09/2.62 Lemma 30: join(zero, complement(complement(X))) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 join(zero, complement(complement(X)))
% 17.09/2.62 = { by axiom 6 (def_zero_13) }
% 17.09/2.62 join(meet(X, complement(X)), complement(complement(X)))
% 17.09/2.62 = { by lemma 20 R->L }
% 17.09/2.62 join(meet(X, complement(X)), complement(join(complement(X), complement(X))))
% 17.09/2.62 = { by lemma 26 }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 31: join(X, zero) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 join(X, zero)
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 join(zero, X)
% 17.09/2.62 = { by lemma 27 R->L }
% 17.09/2.62 join(zero, join(zero, meet(X, X)))
% 17.09/2.62 = { by lemma 29 }
% 17.09/2.62 join(meet(X, X), zero)
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.62 join(complement(join(complement(X), complement(X))), zero)
% 17.09/2.62 = { by lemma 20 }
% 17.09/2.62 join(complement(complement(X)), zero)
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.62 join(zero, complement(complement(X)))
% 17.09/2.62 = { by lemma 30 }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 32: join(zero, X) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 join(zero, X)
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 join(X, zero)
% 17.09/2.62 = { by lemma 31 }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 33: complement(complement(X)) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 complement(complement(X))
% 17.09/2.62 = { by lemma 32 R->L }
% 17.09/2.62 join(zero, complement(complement(X)))
% 17.09/2.62 = { by lemma 30 }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 34: meet(Y, X) = meet(X, Y).
% 17.09/2.62 Proof:
% 17.09/2.62 meet(Y, X)
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.62 complement(join(complement(Y), complement(X)))
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 complement(join(complement(X), complement(Y)))
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.09/2.62 meet(X, Y)
% 17.09/2.62
% 17.09/2.62 Lemma 35: complement(join(zero, complement(X))) = meet(X, top).
% 17.09/2.62 Proof:
% 17.09/2.62 complement(join(zero, complement(X)))
% 17.09/2.62 = { by lemma 15 R->L }
% 17.09/2.62 complement(join(complement(top), complement(X)))
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.09/2.62 meet(top, X)
% 17.09/2.62 = { by lemma 34 R->L }
% 17.09/2.62 meet(X, top)
% 17.09/2.62
% 17.09/2.62 Lemma 36: meet(X, top) = X.
% 17.09/2.62 Proof:
% 17.09/2.62 meet(X, top)
% 17.09/2.62 = { by lemma 35 R->L }
% 17.09/2.62 complement(join(zero, complement(X)))
% 17.09/2.62 = { by lemma 32 }
% 17.09/2.62 complement(complement(X))
% 17.09/2.62 = { by lemma 33 }
% 17.09/2.62 X
% 17.09/2.62
% 17.09/2.62 Lemma 37: meet(X, join(complement(Y), complement(Z))) = complement(join(complement(X), meet(Y, Z))).
% 17.09/2.62 Proof:
% 17.09/2.62 meet(X, join(complement(Y), complement(Z)))
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 meet(X, join(complement(Z), complement(Y)))
% 17.09/2.62 = { by lemma 34 }
% 17.09/2.62 meet(join(complement(Z), complement(Y)), X)
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.62 complement(join(complement(join(complement(Z), complement(Y))), complement(X)))
% 17.09/2.62 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.09/2.62 complement(join(meet(Z, Y), complement(X)))
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.62 complement(join(complement(X), meet(Z, Y)))
% 17.09/2.62 = { by lemma 34 R->L }
% 17.09/2.62 complement(join(complement(X), meet(Y, Z)))
% 17.09/2.62
% 17.09/2.62 Lemma 38: complement(join(X, complement(Y))) = meet(Y, complement(X)).
% 17.09/2.62 Proof:
% 17.09/2.62 complement(join(X, complement(Y)))
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 complement(join(complement(Y), X))
% 17.09/2.62 = { by lemma 36 R->L }
% 17.09/2.62 complement(join(complement(Y), meet(X, top)))
% 17.09/2.62 = { by lemma 34 R->L }
% 17.09/2.62 complement(join(complement(Y), meet(top, X)))
% 17.09/2.62 = { by lemma 37 R->L }
% 17.09/2.62 meet(Y, join(complement(top), complement(X)))
% 17.09/2.62 = { by lemma 15 }
% 17.09/2.62 meet(Y, join(zero, complement(X)))
% 17.09/2.62 = { by lemma 32 }
% 17.09/2.62 meet(Y, complement(X))
% 17.09/2.62
% 17.09/2.62 Lemma 39: complement(meet(X, complement(Y))) = join(Y, complement(X)).
% 17.09/2.62 Proof:
% 17.09/2.62 complement(meet(X, complement(Y)))
% 17.09/2.62 = { by lemma 32 R->L }
% 17.09/2.62 complement(join(zero, meet(X, complement(Y))))
% 17.09/2.62 = { by lemma 38 R->L }
% 17.09/2.62 complement(join(zero, complement(join(Y, complement(X)))))
% 17.09/2.62 = { by lemma 35 }
% 17.09/2.62 meet(join(Y, complement(X)), top)
% 17.09/2.62 = { by lemma 36 }
% 17.09/2.62 join(Y, complement(X))
% 17.09/2.62
% 17.09/2.62 Lemma 40: complement(meet(complement(X), Y)) = join(X, complement(Y)).
% 17.09/2.62 Proof:
% 17.09/2.62 complement(meet(complement(X), Y))
% 17.09/2.62 = { by lemma 34 }
% 17.09/2.62 complement(meet(Y, complement(X)))
% 17.09/2.62 = { by lemma 39 }
% 17.09/2.62 join(X, complement(Y))
% 17.09/2.62
% 17.09/2.62 Lemma 41: join(complement(X), complement(Y)) = complement(meet(X, Y)).
% 17.09/2.62 Proof:
% 17.09/2.62 join(complement(X), complement(Y))
% 17.09/2.62 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.62 join(complement(Y), complement(X))
% 17.09/2.62 = { by lemma 27 R->L }
% 17.09/2.62 join(zero, meet(join(complement(Y), complement(X)), join(complement(Y), complement(X))))
% 17.09/2.62 = { by lemma 37 }
% 17.09/2.62 join(zero, complement(join(complement(join(complement(Y), complement(X))), meet(Y, X))))
% 17.09/2.62 = { by lemma 32 }
% 17.09/2.63 complement(join(complement(join(complement(Y), complement(X))), meet(Y, X)))
% 17.09/2.63 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.09/2.63 complement(join(meet(Y, X), meet(Y, X)))
% 17.09/2.63 = { by lemma 34 }
% 17.09/2.63 complement(join(meet(X, Y), meet(Y, X)))
% 17.09/2.63 = { by lemma 34 }
% 17.09/2.63 complement(join(meet(X, Y), meet(X, Y)))
% 17.09/2.63 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.63 complement(join(meet(X, Y), complement(join(complement(X), complement(Y)))))
% 17.09/2.63 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.63 complement(join(complement(join(complement(X), complement(Y))), complement(join(complement(X), complement(Y)))))
% 17.09/2.63 = { by lemma 20 }
% 17.09/2.63 complement(complement(join(complement(X), complement(Y))))
% 17.09/2.63 = { by axiom 11 (maddux4_definiton_of_meet_4) R->L }
% 17.09/2.63 complement(meet(X, Y))
% 17.09/2.63
% 17.09/2.63 Lemma 42: join(X, meet(X, Y)) = X.
% 17.09/2.63 Proof:
% 17.09/2.63 join(X, meet(X, Y))
% 17.09/2.63 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.63 join(X, complement(join(complement(X), complement(Y))))
% 17.09/2.63 = { by lemma 40 R->L }
% 17.09/2.63 complement(meet(complement(X), join(complement(X), complement(Y))))
% 17.09/2.63 = { by lemma 31 R->L }
% 17.09/2.63 complement(join(meet(complement(X), join(complement(X), complement(Y))), zero))
% 17.09/2.63 = { by lemma 15 R->L }
% 17.09/2.63 complement(join(meet(complement(X), join(complement(X), complement(Y))), complement(top)))
% 17.09/2.63 = { by lemma 40 R->L }
% 17.09/2.63 complement(join(meet(complement(X), complement(meet(complement(complement(X)), Y))), complement(top)))
% 17.09/2.63 = { by lemma 23 R->L }
% 17.09/2.63 complement(join(meet(complement(X), complement(meet(complement(complement(X)), Y))), complement(join(complement(Y), top))))
% 17.09/2.63 = { by lemma 16 R->L }
% 17.09/2.63 complement(join(meet(complement(X), complement(meet(complement(complement(X)), Y))), complement(join(complement(complement(X)), join(complement(Y), complement(complement(complement(X))))))))
% 17.09/2.63 = { by lemma 41 }
% 17.09/2.63 complement(join(meet(complement(X), complement(meet(complement(complement(X)), Y))), complement(join(complement(complement(X)), complement(meet(Y, complement(complement(X))))))))
% 17.09/2.63 = { by lemma 34 R->L }
% 17.09/2.63 complement(join(meet(complement(X), complement(meet(complement(complement(X)), Y))), complement(join(complement(complement(X)), complement(meet(complement(complement(X)), Y))))))
% 17.09/2.63 = { by lemma 26 }
% 17.09/2.63 complement(complement(X))
% 17.09/2.63 = { by lemma 33 }
% 17.09/2.63 X
% 17.09/2.63
% 17.09/2.63 Lemma 43: complement(join(complement(X), Y)) = meet(X, complement(Y)).
% 17.09/2.63 Proof:
% 17.09/2.63 complement(join(complement(X), Y))
% 17.09/2.63 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.63 complement(join(Y, complement(X)))
% 17.09/2.63 = { by lemma 38 }
% 17.09/2.63 meet(X, complement(Y))
% 17.09/2.63
% 17.09/2.63 Lemma 44: composition(converse(sk1), complement(sk1)) = zero.
% 17.09/2.63 Proof:
% 17.09/2.63 composition(converse(sk1), complement(sk1))
% 17.09/2.63 = { by lemma 32 R->L }
% 17.09/2.63 join(zero, composition(converse(sk1), complement(sk1)))
% 17.09/2.63 = { by lemma 15 R->L }
% 17.09/2.63 join(complement(top), composition(converse(sk1), complement(sk1)))
% 17.09/2.63 = { by axiom 2 (goals_14) R->L }
% 17.09/2.63 join(complement(top), composition(converse(sk1), complement(composition(sk1, top))))
% 17.09/2.63 = { by lemma 19 }
% 17.09/2.63 complement(top)
% 17.09/2.63 = { by lemma 15 }
% 17.09/2.63 zero
% 17.09/2.63
% 17.09/2.63 Lemma 45: join(meet(X, Y), meet(X, complement(Y))) = X.
% 17.09/2.63 Proof:
% 17.09/2.63 join(meet(X, Y), meet(X, complement(Y)))
% 17.09/2.63 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.63 join(meet(X, complement(Y)), meet(X, Y))
% 17.09/2.63 = { by axiom 11 (maddux4_definiton_of_meet_4) }
% 17.09/2.63 join(meet(X, complement(Y)), complement(join(complement(X), complement(Y))))
% 17.09/2.63 = { by lemma 26 }
% 17.09/2.63 X
% 17.09/2.63
% 17.09/2.63 Lemma 46: join(complement(X), meet(X, Y)) = join(Y, complement(X)).
% 17.09/2.63 Proof:
% 17.09/2.63 join(complement(X), meet(X, Y))
% 17.09/2.63 = { by lemma 34 }
% 17.09/2.63 join(complement(X), meet(Y, X))
% 17.09/2.63 = { by lemma 42 R->L }
% 17.09/2.63 join(join(complement(X), meet(complement(X), Y)), meet(Y, X))
% 17.09/2.63 = { by axiom 10 (maddux2_join_associativity_2) R->L }
% 17.09/2.63 join(complement(X), join(meet(complement(X), Y), meet(Y, X)))
% 17.09/2.63 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.63 join(complement(X), join(meet(Y, X), meet(complement(X), Y)))
% 17.09/2.63 = { by lemma 34 }
% 17.09/2.63 join(complement(X), join(meet(Y, X), meet(Y, complement(X))))
% 17.09/2.63 = { by lemma 45 }
% 17.09/2.63 join(complement(X), Y)
% 17.09/2.63 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.63 join(Y, complement(X))
% 17.09/2.63
% 17.09/2.63 Lemma 47: join(composition(X, Y), composition(Z, Y)) = composition(join(Z, X), Y).
% 17.09/2.63 Proof:
% 17.09/2.63 join(composition(X, Y), composition(Z, Y))
% 17.09/2.63 = { by axiom 12 (composition_distributivity_7) R->L }
% 17.09/2.63 composition(join(X, Z), Y)
% 17.09/2.63 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.63 composition(join(Z, X), Y)
% 17.09/2.63
% 17.09/2.63 Lemma 48: join(meet(X, Y), meet(complement(X), Y)) = Y.
% 17.09/2.63 Proof:
% 17.09/2.63 join(meet(X, Y), meet(complement(X), Y))
% 17.09/2.63 = { by lemma 34 }
% 17.09/2.63 join(meet(X, Y), meet(Y, complement(X)))
% 17.09/2.63 = { by lemma 34 }
% 17.09/2.63 join(meet(Y, X), meet(Y, complement(X)))
% 17.09/2.63 = { by lemma 45 }
% 17.09/2.63 Y
% 17.09/2.63
% 17.09/2.63 Lemma 49: composition(complement(converse(sk1)), meet(sk1, X)) = zero.
% 17.09/2.63 Proof:
% 17.09/2.63 composition(complement(converse(sk1)), meet(sk1, X))
% 17.09/2.63 = { by lemma 31 R->L }
% 17.09/2.63 composition(complement(join(converse(sk1), zero)), meet(sk1, X))
% 17.09/2.63 = { by lemma 15 R->L }
% 17.09/2.63 composition(complement(join(converse(sk1), complement(top))), meet(sk1, X))
% 17.09/2.63 = { by lemma 25 R->L }
% 17.09/2.63 composition(complement(join(converse(sk1), complement(converse(top)))), meet(sk1, X))
% 17.09/2.63 = { by axiom 5 (def_top_12) }
% 17.09/2.63 composition(complement(join(converse(sk1), complement(converse(join(sk1, complement(sk1)))))), meet(sk1, X))
% 17.09/2.63 = { by axiom 9 (converse_additivity_9) }
% 17.09/2.63 composition(complement(join(converse(sk1), complement(join(converse(sk1), converse(complement(sk1)))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 40 R->L }
% 17.09/2.63 composition(complement(complement(meet(complement(converse(sk1)), join(converse(sk1), converse(complement(sk1)))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 41 R->L }
% 17.09/2.63 composition(complement(join(complement(complement(converse(sk1))), complement(join(converse(sk1), converse(complement(sk1)))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 36 R->L }
% 17.09/2.63 composition(complement(join(complement(complement(converse(sk1))), complement(join(converse(sk1), meet(converse(complement(sk1)), top))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 35 R->L }
% 17.09/2.63 composition(complement(join(complement(complement(converse(sk1))), complement(join(converse(sk1), complement(join(zero, complement(converse(complement(sk1))))))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 38 }
% 17.09/2.63 composition(complement(join(complement(complement(converse(sk1))), meet(join(zero, complement(converse(complement(sk1)))), complement(converse(sk1))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 32 }
% 17.09/2.63 composition(complement(join(complement(complement(converse(sk1))), meet(complement(converse(complement(sk1))), complement(converse(sk1))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 34 R->L }
% 17.09/2.63 composition(complement(join(complement(complement(converse(sk1))), meet(complement(converse(sk1)), complement(converse(complement(sk1)))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 46 }
% 17.09/2.63 composition(complement(join(complement(converse(complement(sk1))), complement(complement(converse(sk1))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 41 }
% 17.09/2.63 composition(complement(complement(meet(converse(complement(sk1)), complement(converse(sk1))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 39 }
% 17.09/2.63 composition(complement(join(converse(sk1), complement(converse(complement(sk1))))), meet(sk1, X))
% 17.09/2.63 = { by lemma 38 }
% 17.09/2.63 composition(meet(converse(complement(sk1)), complement(converse(sk1))), meet(sk1, X))
% 17.09/2.63 = { by lemma 34 R->L }
% 17.09/2.63 composition(meet(complement(converse(sk1)), converse(complement(sk1))), meet(sk1, X))
% 17.09/2.63 = { by lemma 32 R->L }
% 17.09/2.63 composition(join(zero, meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.63 = { by lemma 15 R->L }
% 17.09/2.63 composition(join(complement(top), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.63 = { by lemma 23 R->L }
% 17.09/2.63 composition(join(complement(join(converse(converse(complement(converse(sk1)))), top)), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.63 = { by lemma 16 R->L }
% 17.09/2.63 composition(join(complement(join(converse(complement(sk1)), join(converse(converse(complement(converse(sk1)))), complement(converse(complement(sk1)))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by axiom 10 (maddux2_join_associativity_2) }
% 17.09/2.64 composition(join(complement(join(join(converse(complement(sk1)), converse(converse(complement(converse(sk1))))), complement(converse(complement(sk1))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by axiom 9 (converse_additivity_9) R->L }
% 17.09/2.64 composition(join(complement(join(converse(join(complement(sk1), converse(complement(converse(sk1))))), complement(converse(complement(sk1))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by axiom 3 (maddux1_join_commutativity_1) }
% 17.09/2.64 composition(join(complement(join(complement(converse(complement(sk1))), converse(join(complement(sk1), converse(complement(converse(sk1))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by lemma 43 }
% 17.09/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(join(complement(sk1), converse(complement(converse(sk1))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.09/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(join(converse(complement(converse(sk1))), complement(sk1))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by lemma 39 R->L }
% 17.09/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(meet(sk1, complement(converse(complement(converse(sk1))))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by lemma 33 R->L }
% 17.09/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by lemma 31 R->L }
% 17.09/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(join(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))), zero))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.09/2.64 = { by lemma 15 R->L }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(join(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))), complement(top)))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 25 R->L }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(join(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))), complement(converse(top))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by axiom 5 (def_top_12) }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(join(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))), complement(converse(join(converse(complement(complement(sk1))), complement(converse(complement(complement(sk1)))))))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 24 }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(join(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))), complement(join(complement(complement(sk1)), converse(complement(converse(complement(complement(sk1)))))))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 43 }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(join(meet(sk1, complement(converse(complement(converse(complement(complement(sk1))))))), meet(complement(sk1), complement(converse(complement(converse(complement(complement(sk1)))))))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 48 }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(complement(converse(complement(converse(complement(complement(sk1)))))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 33 }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(complement(complement(converse(complement(converse(sk1)))))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 33 }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(converse(converse(complement(converse(sk1)))))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by axiom 4 (converse_idempotence_8) }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), complement(complement(converse(sk1)))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 33 }
% 17.90/2.64 composition(join(meet(converse(complement(sk1)), converse(sk1)), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 34 R->L }
% 17.90/2.64 composition(join(meet(converse(sk1), converse(complement(sk1))), meet(complement(converse(sk1)), converse(complement(sk1)))), meet(sk1, X))
% 17.90/2.64 = { by lemma 48 }
% 17.90/2.64 composition(converse(complement(sk1)), meet(sk1, X))
% 17.90/2.64 = { by lemma 17 R->L }
% 17.90/2.64 converse(composition(converse(meet(sk1, X)), complement(sk1)))
% 17.90/2.64 = { by lemma 32 R->L }
% 17.90/2.64 converse(join(zero, composition(converse(meet(sk1, X)), complement(sk1))))
% 17.90/2.64 = { by lemma 44 R->L }
% 17.90/2.64 converse(join(composition(converse(sk1), complement(sk1)), composition(converse(meet(sk1, X)), complement(sk1))))
% 17.90/2.64 = { by axiom 12 (composition_distributivity_7) R->L }
% 17.90/2.64 converse(composition(join(converse(sk1), converse(meet(sk1, X))), complement(sk1)))
% 17.90/2.64 = { by axiom 9 (converse_additivity_9) R->L }
% 17.90/2.64 converse(composition(converse(join(sk1, meet(sk1, X))), complement(sk1)))
% 17.90/2.64 = { by lemma 42 }
% 17.90/2.64 converse(composition(converse(sk1), complement(sk1)))
% 17.90/2.64 = { by lemma 44 }
% 17.90/2.64 converse(zero)
% 17.90/2.64 = { by lemma 31 R->L }
% 17.90/2.64 join(converse(zero), zero)
% 17.90/2.64 = { by lemma 29 R->L }
% 17.90/2.64 join(zero, join(zero, converse(zero)))
% 17.90/2.64 = { by lemma 24 R->L }
% 17.90/2.64 join(zero, converse(join(converse(zero), zero)))
% 17.90/2.64 = { by lemma 31 }
% 17.90/2.64 join(zero, converse(converse(zero)))
% 17.90/2.64 = { by axiom 4 (converse_idempotence_8) }
% 17.90/2.64 join(zero, zero)
% 17.90/2.64 = { by lemma 28 }
% 17.90/2.64 zero
% 17.90/2.64
% 17.90/2.64 Goal 1 (goals_15): composition(meet(sk2, converse(sk1)), meet(sk1, sk3)) = composition(sk2, meet(sk1, sk3)).
% 17.90/2.64 Proof:
% 17.90/2.64 composition(meet(sk2, converse(sk1)), meet(sk1, sk3))
% 17.90/2.64 = { by lemma 31 R->L }
% 17.90/2.64 join(composition(meet(sk2, converse(sk1)), meet(sk1, sk3)), zero)
% 17.90/2.64 = { by lemma 49 R->L }
% 17.90/2.64 join(composition(meet(sk2, converse(sk1)), meet(sk1, sk3)), composition(complement(converse(sk1)), meet(sk1, sk3)))
% 17.90/2.64 = { by lemma 47 }
% 17.90/2.64 composition(join(complement(converse(sk1)), meet(sk2, converse(sk1))), meet(sk1, sk3))
% 17.90/2.64 = { by lemma 34 }
% 17.90/2.64 composition(join(complement(converse(sk1)), meet(converse(sk1), sk2)), meet(sk1, sk3))
% 17.90/2.64 = { by lemma 46 }
% 17.90/2.64 composition(join(sk2, complement(converse(sk1))), meet(sk1, sk3))
% 17.90/2.64 = { by axiom 3 (maddux1_join_commutativity_1) R->L }
% 17.90/2.64 composition(join(complement(converse(sk1)), sk2), meet(sk1, sk3))
% 17.90/2.64 = { by lemma 47 R->L }
% 17.90/2.64 join(composition(sk2, meet(sk1, sk3)), composition(complement(converse(sk1)), meet(sk1, sk3)))
% 17.90/2.64 = { by lemma 49 }
% 17.90/2.64 join(composition(sk2, meet(sk1, sk3)), zero)
% 17.90/2.64 = { by lemma 31 }
% 17.90/2.64 composition(sk2, meet(sk1, sk3))
% 17.90/2.64 % SZS output end Proof
% 17.90/2.64
% 17.90/2.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------